Deadlift is an excellent exercise for the whole "Posterior chain" (i.e. the whole system of back, glutes and legs), see picture below.

I find it easier to understand it in terms of the wholeness instead of individual muscles. So, it is not an exercise only for the legs or the back which is why you sometimes see people having problems with fitting it in a "upper body" and "lower body" workout routine.

It is dangerous to deadlift without a belt because of potential herniation of the stomach or back lining! I don't think its a thing that can really be decided for personal preference. If you are lifting light (up to about 300 pounds) you could probably get away with it but any more than that and you are forcing too much pressure against your abdominal wall. I've lifted 465 with no gear just to see if I could do it (and I could). It doesn't make any difference in your strength, it just makes you more confident that you won't break something.
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Mike SNov 1 '12 at 22:54

Mike, yeah that correct it gives more confident,Exactly what area i need to wear belt?
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Prince Antony GNov 2 '12 at 6:05

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@MikeS Serious question, do you have any experience with deadlifting causing hernias, or studies, or anecdotes, or even an explanation from someone familiar with both the science and the lifting?
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Dave LiepmannNov 4 '12 at 4:26

No @DaveLiepmann I've never studied it actually. I just know people sometimes get hernias when lifting things. Since a deadlift/squat is the heaviest thing you are ever going to lift, it makes sense to get some protection. Whenever I forget my belt and deadlift without it, I always get personal trainers coming up to me asking me to wear a belt. See if you can find a powerlifter competing without a belt!!
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Mike SNov 4 '12 at 22:24

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@PrinceAntonyG I wear mine across my belly button. Be sure to get a nice thick one.
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Mike SNov 4 '12 at 22:28

The latissimus dorsi extends the shoulder joint - meaning it brings the elbows from overhead to near the body. When you're deadlifting, the lats work really hard because you need to keep the bar close to your body. If your form is correct, the lats will be hit hard.

If the pain you felt was muscle burn and not anything related to injury, that's ok. But, maybe the bar is a bit too much away from you at the beginning of the movement. Try getting in position so the part of your feet where your shoelaces are is under the bar, and your shin touches it a bit. Make sure your back is straight and your upper back is tight. You don't "need" to do any exercise, but the deadlift is a great one because it works a huge amount of muscle.

To answer your questions:

The deadlift is usually classified as a back exercise, although I'd say it's literally a "back exercise" because it works every muscle on the back of your body from your feet to your neck! Everything there gets a good beating.
But I'd never say it's a leg exercise, or for shaping the legs. The reason is, the main movers are the spinal erectors (lower back), the glutes and the hamstrings. Only the hamstrings are really a part of the leg, and they could be better hit with the romanian deadlift, for example. There's no doubt the deadlift will give you powerful hamstrings, but it will mainly give you a big back.

You don't. The belt is here to keep your entire core tight - but you can do that on your own. If your core isn't tight you could get hernia. But you'd need to lift really really heavy weights for that to happen. I never use the belt myself.